Large-angle inelastic electron scattering from adsorbate vibrations: Basic theory

This paper formulates the theory of large-angle inelastic electron scattering from vibrational motions of the crystal surface. We focus attention on the scattering from an ordered overlayer of adsorbed molecules, but the formulation developed here is applicable to a variety of other situations, so long as the surface structure is periodic. The emphasis is on incorporation of multiple scattering of the electron from the adsorbate-substrate combination as it either approaches or exits from a site where vibrational excitation occurs. The method here makes explicit contact with earlier theories of low-energy electron diffraction from surfaces, and theories of angle-resolved photoemission. By synthesizing elements of these theories with a model of the electron-phonon coupling, we obtain general expressions for the energy variation of the inelastic cross section and its angular variation. A separate paper reports a series of numerical calculations based on the present formalism for a $c(2\mathrm{}\times 2)$ overlayer of CO on the Ni(100) surface.